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Areal Parabolic Centroid

For a Parabola y2=24xy^2 = 24x, consider all chords PQPQ of the parabola such that the chords make a constant area A>12A \gt 12 with the parabola. The vertex of above parabola is OO.

Find locus of centroid of ΔOPQ\Delta OPQ. Length of Latus Rectum of locus is LL and coordinates of focus of locus is S(x,y)S(x, y).

If L=a,x>b,y=cL = a, x \gt b, y = c, Enter answer as a+b+ca + b + c

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